# Privacy-Preserving Federated Learning via System Immersion and Random Matrix Encryption

arXiv: https://arxiv.org/abs/2204.02497 · HTML: https://mlsanity.com/paper/2204.02497/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 15 of 15)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [A Hybrid Approach to Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1812.03224/) (2018)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [Comprehensive Privacy Analysis of Deep Learning: Passive and Active White-box Inference Attacks against Centralized and Federated Learning](https://mlsanity.com/paper/1812.00910/) (2018)
- [HybridAlpha: An Efficient Approach for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1912.05897/) (2019)
- [Privacy-preserving Federated Learning based on Multi-key Homomorphic Encryption](https://mlsanity.com/paper/2104.06824/) (2021)
- [CaPC Learning: Confidential and Private Collaborative Learning](https://mlsanity.com/paper/2102.05188/) (2021)
- [A Scalable Approach for Privacy-Preserving Collaborative Machine Learning](https://mlsanity.com/paper/2011.01963/) (2020)
- [Finite Horizon Privacy of Stochastic Dynamical Systems: A Synthesis Framework for Dependent Gaussian Mechanisms](https://mlsanity.com/paper/2108.01755/) (2021)

## Built on by (most cited first, 1 of 1)

- [Immersion and Invariance-based Coding for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2409.17201/) (2024)

## Abstract (arXiv)

Federated learning (FL) has emerged as a privacy solution for collaborative distributed learning where clients train AI models directly on their devices instead of sharing their data with a centralized (potentially adversarial) server. Although FL preserves local data privacy to some extent, it has been shown that information about clients' data can still be inferred from model updates. In recent years, various privacy-preserving schemes have been developed to address this privacy leakage. However, they often provide privacy at the expense of model performance or system efficiency, and balancing these tradeoffs is a crucial challenge when implementing FL schemes. In this manuscript, we propose a Privacy-Preserving Federated Learning (PPFL) framework built on the synergy of matrix encryption and system immersion tools from control theory. The idea is to immerse the learning algorithm, a Stochastic Gradient Decent (SGD), into a higher-dimensional system (the so-called target system) and design the dynamics of the target system so that: the trajectories of the original SGD are immersed/embedded in its trajectories, and it learns on encrypted data (here we use random matrix encryption). Matrix encryption is reformulated at the server as a random change of coordinates that maps original parameters to a higher-dimensional parameter space and enforces that the target SGD converges to an encrypted version of the original SGD optimal solution. The server decrypts the aggregated model using the left inverse of the immersion map. We show that our algorithm provides the same level of accuracy and convergence rate as the standard FL with a negligible computation cost while revealing no information about the clients' data.